Calculus augmented matrix

Question

On the augmented matrix A below , perform all three row operations in the order given, ((a) followed by (b) followed by (c)) and then write the resulting augmented matrix.

(a) r2 <- r2 - 2r1

(b r3 <- r3 + 4r1

(c) r3 <- r3 + 2r2

A = [1 -1 3 | -2 ]

[2 -1 -2 | -2 ]

[-4 2 6 | -2 ]

Answer 1

Step A: r2 - 2r1

[ 1 -1  3 | -2 ]

[ 0  1 -8 |  2 ]

[-4  2  6 | -2 ]

Step B: r3 + 4r1

[ 1 -1   3 |  -2 ]

[ 0  1  -8 |   2 ]

[ 0 -2 18 | -10 ]

Step C: r3 + 2r2

[ 1 -1  3 | -2 ]

[ 0  1 -8 |  2 ]

[ 0  0  2 | -6 ]

The given steps are moving this matrix towards reduced row echelon form. The following steps would finish the process:

r1 + r2

[ 1 0 -5 |  0 ]

[ 0 1 -8 |  2 ]

[ 0 0  2 | -6 ]

r3 / 2

[ 1 0 -5 |  0 ]

[ 0 1 -8 |  2 ]

[ 0 0  1 | -3 ]

r1 + 5r3

[ 1 0  0 | 15 ]

[ 0 1 -8 |  2 ]

[ 0 0  1 |  -3 ]

r2 + 8r3

[ 1 0 0 |  15 ]

[ 0 1 0 | -22 ]

[ 0 0 1 |   -3 ]

Answer 2

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